TY - JOUR
ID - 57
TI - Asymptotic behaviour of associated primes of monomial ideals with combinatorial applications
JO - Journal of Algebra and Related Topics
JA - JART
LA - en
SN - 2345-3931
AU - Nasernejad, M.
AD - University of Payame Noor
Y1 - 2014
PY - 2014
VL - 2
IS - 1
SP - 15
EP - 25
KW - Monomial ideals
KW - associated prime ideals
KW - trees
KW - paths
DO -
N2 - Let $R$ be a commutative Noetherian ring and $I$ be an ideal of $R$. We say that $I$ satisfies the persistence property if $mathrm{Ass}_R(R/I^k)subseteq mathrm{Ass}_R(R/I^{k+1})$ for all positive integers $kgeq 1$, which $mathrm{Ass}_R(R/I)$ denotes the set of associated prime ideals of $I$. In this paper, we introduce a class of square-free monomial ideals in the polynomial ring $R=K[x_1,ldots,x_n]$ over field $K$ which are associated to unrooted trees such that if $G$ is a unrooted tree and $I_t(G)$ is the ideal generated by the paths of $G$ of length $t$, then $J_t(G):=I_t(G)^vee$, where $I^vee$ denotes the Alexander dual of $I$, satisfies the persistence property. We also present a class of graphs such that the path ideals generated by paths of length two satisfy the persistence property. We conclude this paper by giving a criterion for normally torsion-freeness of monomial ideals.
UR - https://jart.guilan.ac.ir/article_57.html
L1 - https://jart.guilan.ac.ir/article_57_45c5e51de657c1dc081bfad7d1fc6b80.pdf
ER -